一类具连续时滞的捕食-被捕食生态系统

本文讨论了一类具有强连续时滞的捕食-被捕食模型,分析了各非负平衡点的稳定性,利用区域连续收缩方法,得出非负平衡点全局稳定的充分条件,给出正平衡点全局稳定的充分条件,并给出系统出现Hopf的分支值．     

具有时滞的HBV病毒动力学模型稳定性分析

HBV（HePatitis B virus）是一种具有严重传染性的肝炎病毒,迄今为止,人们对它的免疫和慢性化的机制等方面还不甚了解。本文基于相关的病理知识,对应的建立了具有时滞的微分方程数学模型,系统地探讨了肝炎B病毒与宿主细胞之间的关系,利用Lyapunov函数方法研究了病毒动力学模型感染平衡点的局部稳定性和未感染平衡点全局稳定性,并利用数学模拟验证了理论分析。结果表明时滞的存在不会影响到感染平衡点的局部稳定性,但能影响平衡点到达的时间跨度,对于药物治疗的疗程和治疗时机的确定有参考意义。     

REVIEW: Time lag between photosynthesis and carbon dioxide efflux from soil: a review of mechanisms and controls

CO₂ efflux from soil depends on the availability of organic substances respired by roots and microorganisms. Therefore, photosynthetic activity supplying carbohydrates from leaves to roots and rhizosphere is a key driver of soil CO₂. This fact has been overlooked in most soil CO₂ studies because temperature variations are highly correlated with solar radiation and mask the direct effect of photosynthesis on substrate availability in soil. This review highlights the importance of photosynthesis for rhizosphere processes and evaluates the time lag between carbon (C) assimilation and CO₂ release from soil. Mechanisms and processes contributing to the lag were evaluated. We compared the advantages and shortcomings of four main approaches used to estimate this time lag: (1) interruption of assimilate flow from leaves into the roots and rhizosphere, and analysis of the decrease of CO₂ efflux from soil, (2) time series analysis (TSA) of CO₂ fluxes from soil and photosynthesis proxies, (3) analysis of natural δ¹³C variation in CO₂ with photosynthesis‐related parameters or δ¹³C in the phloem and leaves, and (4) pulse labeling of plants in artificial ¹⁴CO₂ or ¹³CO₂ atmosphere with subsequent tracing of ¹⁴C or ¹³C in CO₂ efflux from soil. We concluded that pulse labeling is the most advantageous approach. It allows clear evaluation not only of the time lag, but also of the label dynamics in soil CO₂, and helps estimate the mean residence time of recently assimilated C in various above‐ and belowground C pools. The impossibility of tracing the phloem pressure–concentration waves by labeling approach may be overcome by its combination with approaches based on TSA of CO₂ fluxes and its δ¹³C with photosynthesis proxies. Numerous studies showed that the time lag for grasses is about 12.5±7.5 (SD) h. The time lag for mature trees was much longer (～4–5 days). Tree height slightly affected the lag, with increasing delay of 0.1 day m^?1. By evaluating bottle‐neck processes responsible for the time lag, we conclude that, for trees, the transport of assimilates in phloem is the rate‐limiting step. However, it was not possible to predict the lag based on the phloem transport rates reported in the literature. We conclude that studies of CO₂ fluxes from soil, especially in ecosystems with a high contribution of root‐derived CO₂, should consider photosynthesis as one of the main drivers of C fluxes. This calls for incorporating photosynthesis in soil C turnover models.     

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator

A three-dimensional stage-structured predator–prey model is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with non-constant harvesting. Time lag in maturation of the predator is introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a supercritical Hopf bifurcation when the maturation time lag crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.     

一类生态系统的平衡点的绝对稳定性

本文对具有两个确定时滞的一类生态系统模型进行了讨论,得到了其平衡点绝对稳定的充分条件。     

具有时滞和阶段结构的捕食-被捕食模型及最优捕获策略

研究了一个具有阶段结构和时滞的捕食-被捕食模型.分析了它的局部性质。得到某些非负平衡点全局稳定的充分条件,其中用到李雅普诺夫函数及其他方法．最后,在内部平衡点全局稳定的情况下,得出了最优捕获策略．     

Electromechanical delay in isometric muscle contractions evoked by voluntary, reflex and electrical stimulation

Electromechanical delay (EMD) in isometric contractions of knee extensors evoked by voluntary, tendon reflex (TR) and electrical stimulation (ES) was investigated in 21 healthy young subjects. The subject performed voluntary knee extensions with maximum effort (maximal voluntary contraction, MVC), and at 30%, 60% and 80% MVC. Patellar tendon reflexes were evoked with the reflex hammer being dropped from 60°, 75° and 90° positions. In the percutaneous ES evoked contractions, single switches were triggered with pulses of duration 1.0 ms and of intensities 90, 120 and 150 V. Electromyograms of the vastus lateralis and rectus femoris muscles were recorded using surface electrodes. The isometric knee extension force was recorded using a load cell force transducer connected to the subject's lower leg. The major finding of this study was that EMD of the involuntary contractions [e.g. mean 22.1 (SEM 1.32) ms in TR 90°; mean 17.2 (SEM 0.62) ms in ES 150 V] was significantly shorter than that of the voluntary contractions [e.g. mean 38.7 (SEM 1.18) ms in MVC,P < 0.05]. The relationships between EMD, muscle contractile properties and muscle fibre conduction velocity were also investigated. Further study is needed to explain fully the EMD differences found between the voluntary and involuntary contractions.     

具反馈控制的时滞阶段结构种群模型的稳定性

研究具反馈控制的时滞阶段结构种群模型,证明了正平衡点的局部渐近稳定性, 并给出了正平衡点全局渐近稳定的充分条件．